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Spatial latent class analysis model for spatially distributed multivariate binary data

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  • Wall, Melanie M.
  • Liu, Xuan

Abstract

A spatial latent class analysis model that extends the classic latent class analysis model by adding spatial structure to the latent class distribution through the use of the multinomial probit model is introduced. Linear combinations of independent Gaussian spatial processes are used to develop multivariate spatial processes that are underlying the categorical latent classes. This allows the latent class membership to be correlated across spatially distributed sites and it allows correlation between the probabilities of particular types of classes at any one site. The number of latent classes is assumed to be fixed but is chosen by model comparison via cross-validation. An application of the spatial latent class analysis model is shown using soil pollution samples where 8 heavy metals were measured to be above or below government pollution limits across a 25 square kilometer region. Estimation is performed within a Bayesian framework using MCMC and is implemented using the OpenBUGS software.

Suggested Citation

  • Wall, Melanie M. & Liu, Xuan, 2009. "Spatial latent class analysis model for spatially distributed multivariate binary data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3057-3069, June.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:3057-3069
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    6. Solaiman Afroughi & Soghrat Faghihzadeh & Majid Jafari Khaledi & Mehdi Ghandehari Motlagh & Ebrahim Hajizadeh, 2011. "Analysis of clustered spatially correlated binary data using autologistic model and Bayesian method with an application to dental caries of 3--5-year-old children," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2763-2774, February.
    7. Jian Kang & Nanhua Zhang & Ran Shi, 2014. "A Bayesian nonparametric model for spatially distributed multivariate binary data with application to a multidrug-resistant tuberculosis (MDR-TB) study," Biometrics, The International Biometric Society, vol. 70(4), pages 981-992, December.

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